The beautiful integration. Let us go through each picture of the GIF step by step.
- You originally see a sphere.
- The sphere meshes in many pieces.
- It then explodes and simultaneously changes from 3 dimensions to 2 dimensions.
- The upper half becomes the positive part of the sine wave.
- The lower half becomes the negative part of the sine wave.
- This sine wave is then integrated over the axis it is projected on.(in this case the x-axis)
- And magic: You get the area of the sphere which IS 4*pi*r squared.